Collision of an Atom and a Diatomic. The Adiabatic Approximation

The adiabatic approximation is used to compute vibrational transition probabilities for the collision of an atom and a diatomic molecule in one dimension. The accuracy of the results is evaluated in terms of a parameter β, which is proportional to the period of the oscillator divided by the length of the collision. It is seen that for small β, the error in adiabatic transition probabilities approaches zero, and that the approximation is accurate over a physically interesting range of β.